garden building advice under the permitted delovopment right

We are facing a significant issue with our Chinese supplier regarding the delivery of our flat-pack garden building, which we intended to construct in compliance with permitted development rights. The building's specifications require a gutter height of 2500mm and a dual-pitched roof height of 1500mm, resulting in a total height of 4000mm. However, the supplier provided a main frame height of 2800mm, which has raised the gutter height by 300mm.

The front of the building will feature double-glazed glass supplied by the manufacturer. Due to the high cost of the glass panels, we cannot simply lower the frame, as the current panels would not fit. Additionally, altering the glass panels would not work either as there double glassed units in metal frames. The obvoius option would be to lower the frame to 2500mm and have all the glass remade, but unfortunately, we do not have the funds to cover this expense.

As an alternative, we are considering overhanging the roof and boxing it in to decrease the gutter height. Would this solution likely be acceptable under the permitted building regulations? I have added a diagram to show what i mean

The other issue we have is we have now been advised we need keep 2000mm gap between the L shape building and the boundry walls of the garden, The largest section of the building that runs along the back of the garden there is a 2000mm plus gap from the rear wall, the problem occurs with section of building on the left this is virtually touching the side boundry wall in areas, we were wondering if it would be at all possible to alter the design possibly maybe have two separate buildings in theory and have the side part of the building as more like a gazebo so four pilers and a roof or even a seperate 3 sided building however im not sure if a 3 sided building with the opening to the front would be acceptable to be considered under the permited building act , this side section was already going to have the front open, its actually going to be a outdoor kitchen, we were wondering if it was a separate building with either no walls or three walls and not connected to the rear section if this would enable us not to require the 2000mm, as its not a building as such,

I would like to mention that I pursued planning permission, as advised by the planning enforcement officer. This process cost me hundreds of pounds in fees and technical drawings, but my application was completely refused since we are in a conservation area next to a Grade 1 listed building. I have been advised to proceed with the permitted development route, which should allow me to move forward without further issues. I don’t require any drawings; I just need some advice so I can continue with my project.